In this paper, a system has been designed for an operational frequency of 1.27 GHz consisting of an 8 element array of parasitic dipoles illuminated by a 4 element center fed array of active dipoles with Dolph-Chebyshev excitation coefficients. The array is designed to achieve a fairly pencil beam pattern suitable for direction of arrival estimation purposes. Array geometry and configuration is optimized for both active and parasitic elements using the PSO tool in FEKO. A directive radiation pattern is obtained with a gain of 14.5 dBi in the broadside direction along with a beamwidth of 30.29o. VSWR of 1.58 is achieved. Further, an iterative least square valued error estimation approach using phase control to achieve a desired array factor pattern for an n-element linear array, has been shown to be effective for larger number of iterations. The array excitation coefficients achieved were consistent with the Dolph-Chebyshev coefficients used in our antenna array design. With the ability to introduce nulls and steering the main beam in desired directions along with a pencil beam radiation pattern, beamsteering has been illustrated and the MUSIC algorithm for direction of arrival estimation has been implemented

1. 1
Abstract— In this paper, a system has been designed for an
operational frequency of 1.27 GHz consisting of an 8 element array of
parasitic dipoles illuminated by a 4 element center fed array of active
dipoles with Dolph-Chebyshev excitation coefficients. The array is
designed to achieve a fairly pencil beam pattern suitable for direction
of arrival estimation purposes. Array geometry and configuration is
optimized for both active and parasitic elements using the PSO tool in
FEKO. A directive radiation pattern is obtained with a gain of 14.5
dBi in the broadside direction along with a beamwidth of 30.29o
.
VSWR of 1.58 is achieved. Further, an iterative least square valued
error estimation approach using phase control to achieve a desired
array factor pattern for an n-element linear array, has been shown to
be effective for larger number of iterations. The array excitation
coefficients achieved were consistent with the Dolph-Chebyshev
coefficients used in our antenna array design. With the ability to
introduce nulls and steering the main beam in desired directions
along with a pencil beam radiation pattern, beamsteering has been
illustrated and the MUSIC algorithm for direction of arrival
estimation has been implemented.
Index Terms—Linear Parasitic Array; Pattern Synthesis; Beam
Steering; DOA Estimation; MUSIC Algorithm
I. INTRODUCTION
Antenna arrays are increasingly being used for a variety of
applications due to their ability to control certain parameters of the
radiation pattern like pattern maximum steering, null angle
placement, increasing the Signal to Interference plus Noise ratio. A
pencil beam radiation pattern is generally obtained by increasing
the effective size of the active array by increasing the number of
elements and element spacing. However this leads to increased
cost, size and complexity. A workaround to this problem is to
make use of the mutual coupling between active and parasitic
elements in the array that allows us to use lesser active feed
elements. This technique also allows parasitic array elements to
introduce degrees of freedom that ensure that pattern can be
synthesized without modification of the active array feed.
Therefore, an 8 element array of parasitic dipoles is illuminated by
a 4 element active array above a finite ground plane to obtain a
pencil beam pattern and its characteristics are observed.
Furthermore, the pattern synthesis problem is crucial to any
array design problem. The desired pattern synthesis problem using
an iterative technique to get a desired radiation pattern is shown to
improve for larger iterations. With the ability to introduce nulls
and steer the beam, Beam steering by changing phases is observed
and the MUSIC algorithm is shown to effectively estimate the
angle of arrival.
II. DESIGN PROCEDURE
We look at the geometry of active/parasitic array combinations
which can be optimized to achieve the desired performance. We
consider the synthesis of low-sidelobe sum patterns generated by
antennas consisting of a parasitic linear array of half-wavelength
dipoles illuminated by similar uniformly fed active array. A real
non-infinite ground plane is included to increase the overall
directivity of the radiation pattern. The parameters which are
manipulated for the pattern synthesis are the distance of the
respective arrays from the ground, distance between adjacent
dipoles in each array and distance between the two arrays. The
effect of mutual coupling between the elements has been taken
care of and accounted by means of FEKO simulation with PSO
optimization. The proposed method is based on the optimization of
the array geometry in order to obtain a highly directive pattern. A
uniformly spaced planar array of parasitic dipoles of length λ/2 is
considered as a starting point in the optimization process. In this
procedure, the distance between the planar array and the ground
plane and the interspacing in the x-axis direction of the parasitic
array are modified. The aim is to find the optimal array geometry
that fulfill the requirements of a given design problem. The
variables mentioned above were optimized by means of PSO to
minimize a cost function C consisting of a term to increase the
directivity in the broadside (Θ=00
, Φ=00
):
C = 1/Directivity (D0) (1)
Taking into account the optimized values we consider an
antenna system consisting of 1.) A non-infinite ground in the x-y
plane with moist soil dielectric whose εr = 30 and tan δ = 0.007;
2.)A linear array of 4 center-fed half-wavelength wire dipoles
oriented parallel and above the x-y plane at a height hactive = λ/4
with their centers located at regular intervals of λ/2 along a line and
3.) A similar linear array of 8 parasitic elements arranged along the
line in the x-y plane at a height hparasitic= 5λ/4. The active dipoles
are excited according to the Dolph-Chebyshev array excitation
coefficients and these have been found out for a 4-element array
system with a side-lobe level to be 30 dB down from the main lobe.
If vector I represents the current distribution on this antenna then it
is given by
I = Z-1
V (2)
where V is the vector of voltages (Vn=22.22 or 9.53 if the element
n is active; Vn=0 if it is parasitic) and Z is the impedance matrix.
Figure 1: Antenna Array Design Schematic with real ground
III. PATTERN SYNTHESIS
Beam forming allows placement of single or multiple nulls in the
antenna pattern at specific interference directions. Prescribed nulls
in the radiation pattern are formed to suppress interferences from
specific directions. For broadband interference, null in the pattern
should be wide and deep enough to suppress peak side lobe levels
at the angular sector of arrival of interference. Nulling methods are
based on controlling complex weights. Having already achieved a
directive pattern for the Dolph-Chebyshev amplitude coefficient
arrangement, we have focused on optimizing array coefficients
further by using phase control.
Designing a pencil beam pattern with low
sidelobes using pattern synthesis technique and a
system of active linear array illuminating
parasitic dipoles
Gaurav Narula(1)
, Piyush Kashyap(2)
(1)(2)
Graduate Student, ECEE Department,
University of Colorado at Boulder
Boulder, CO 80309
United States
(1)
gana2553@colorado.edu, (2)
pika7816@colorado.edu

2. 2
The problem considered is as follows. We want to find a weight
vector W for which the array factor has a beam maximum at some
angle ϴd and meets a given side lobe specification for other angles.
The prerequisites to this problem i.e. number of elements (n) of the
array, element spacing (d), and element patterns are obtained from
the array design performed in FEKO. Consider an n element linear
array as shown in Figure 2. Let fi(ϴ) be the pattern element of each
element.
Figure 2: N-element Linear Array
Let X be the received signal vector with xi(t) being the received
signal on ith element.
X=[x1(t), x2(t), x3(t)….. xn(t)]T
(3)
The array output signal s(t) can be obtained using the following
expression:
s(t) = WT
X (4)
where, W is the weight vector,
X = Aejωo
U is the received signal vector with xi(t) the received
signal on ith element.
Effective array output can be expressed as:
s(t)= Aejω0
WT
U (5)
where A is the signal amplitude, U is a vector that includes inter
element phase shifts and pattern defined as follows
U=[f1 (ϴ) , f2 (ϴ) e-jϕ2(ϴ)
, f3 (ϴ) e –jϕ3(ϴ)
…… fn (ϴ) e–jϕn(ϴ)
]T
dk (6)
The algorithm we deploy to get desired nulls and maxima
essentially finds the vector W for which p(ϴ) = WT
U has a beam
maximum at desired angle ϴd and nulls at other angles. As given in
[9] ,the expression obtained for the weight vector is given by
W = µϕu
-1
Ud
*
(7)
where, Ud is vector of signal from desired direction, Ud
*
is
conjugate of Ud, µ is an arbitrary non zero scalar, ϕu is covariance
matrix of undesired signal, Ui is matrix specified in (8) with ϴ=ϴi
and Ai is the interference amplitude.
Computations based on above formulae are performed on
MATLAB for introducing a null by introducing interference signal
at a specific or range of angles as shown in Fig. 3 and Fig. 4.
(a)
(b)
Figure 3: Adapted patterns with one interference signal at ϴ = π/4 for n =
4element array with ideal isotropic elements (a) INR= -10 dB (b) INR = 10 dB.
These plots show Power variation (in dB) with angle ϴ (in degrees).
Using an iterative technique and the formulations given in [9] the
approach for desired pattern synthesis problem is as follows:
1. The main beam is steered in the desired direction by choosing a
steering vector Ud.
2. To reduce side lobes, a large number of interference signals are
assumed to be incident on the array from side lobe region. Matrix
Ui is generated.
3. Interference amplitude matrix Ai with 32 different combinations
of random numbers is formed to form a pattern P.
4. An adapted weight matrix is created that contains phase
coefficients to be multiplied with each element of the array to get
the desired pattern.
5. 32 adapted patterns are obtained and compared with the design
objective to get an Error matrix.
6. For next iteration, combination with 16 least valued errors are
used as elements of matrix Ai and 16 other random patterns are
obtained using the next16 random numbers in Ai.
After desired number of iterations, of the 32 patterns obtained, the
Weight matrix Wand Interference amplitude matrix Ai for the one
with least deviation is used for the pattern synthesis of the array.
An increase in the number of iterations leads to a better pattern as
shown in Figure 5 where 100 iterations brings down the sidelobe
levels by 10.43 dB approximately.
(a)
(b)
Figure 4: Adapted patterns with 21 interference signals from ϴ = -20o
to -60o
for an 8 element linear array with isotropic elements (a) INR = -10 dB (b) INR
= 10 dB. These plots show Power variation (in dB) with angle ϴ (in degrees).

3. 3
(a)
(b)
(c)
Figure 5: Patterns obtained by the Iteration techniques taking least value
squared error values between desired pattern and obtained patterns (a) Desired
Pattern (b) 100th
iteration (c) 50th
iteration. These plots show Power variation
(in dB) with angle ϴ (in degrees).
IV. RESULTS AND DISCUSSION
A. Gain
The structure parameters have been chosen in such a way that the
VSWR obtained is less than 2 and the antenna gain is maximized
at the frequency of operation. The value of gain obtained is 14.5
dBi as shown below in Figure 7.
Figure 7: Far field Gain pattern for antenna array with real ground plane
B. Radiation Pattern, Beamwidth and VSWR
The E-plane radiation pattern obtained for our antenna array at
operational frequency is below shown in Figure 8.
Figure 8: Electric Field radiation pattern for our antenna array system
At 1.27 GHz, the Half-Power Beamwidth, of our antenna array is
about 30.29o
. This is shown below in Figure 9.
Figure 9: 3dB Beamwidth of antenna array system
VSWR obtained at 1.27 GHz is 1.58, as shown in Figure 10.
Figure 10: VSWR vs Frequency
C. 2:1 VSWR Bandwidth
The obtained 2:1 VSWR bandwidth for our antenna array system is
282 MHz as shown below in the Figure 11.
Figure 11: 2:1 VSWR Bandwidth
D. Performance of antenna array with no parasitic elements
Comparing the results obtained for our antenna array system to that
when there are no parasitic dipoles present in our antenna we found
that, at operational frequency, gain gets reduced to11.5 dBi so as
the directivity. As a result, the 3 dB beamwidth increases to 38.290
.
Values of VSWR and Reflection Coefficient increase to 3.45 and
0.55, respectively. We conclude that using parasitic array of
dipoles does help us achieve substantially better antenna
performance in terms of increase gain (or directivity) and low
reflection coefficient.
E. Effect of height of active and parasitic array from the ground
and distance between the elements
Here we changed the value of hparasitic from 5λ/4 to 3λ/4 and
generated a curve for reflection coefficient which shows a drastic
change in the value of ρ. The new value of reflection coefficient
obtained is about 0.73. This is shown below in Figure 12.
Figure 12: 3dB Beamwidth when hparasitic = 3λ/4

4. 4
Also, the directivity of antenna array gets reduced to 12.7 dBi and
as a result beamwidth of antenna array increases to 40.780
. VSWR
increases to 6.24.
V. VALIDATION
As is expected, increasing the number of active dipoles in the array
will improve the performance. This has been shown in [3]. The
same can be validated in Table 1 for a fixed parasitic/active ratio of
M/N. However , for a given number of active dipoles, increasing
the number of parasitic dipoles only improves performance upto a
M/N ratio of about 2 [3] . This is validated in Table 2. Table 1 and
Table 2 are obtained by simulation on FEKO for different number
of active and parasitic dipoles.
M N M/N Directivity(dBi) BW(o
) VSWR
12 6 2 15.7 24.21 1.56
8 4 2 14.5 30.29 1.58
4 2 2 12.7 38.66 1.74
Table 1: Performance variation with change in number of active elements for a
fixed parasitic to active elements ratio (For constant M:N)
M N M/N Directivity(dBi) BW(o
) VSWR
2 4 0.5 13.8 34.395 2.24
4 4 1 14.2 31.39 1.76
6 4 1.5 14.4 30.76 7.68
8 4 2 14.5 30.29 1.58
10 4 2.5 14.5 30.55 1.59
12 4 3 14.5 30.48 1.59
Table 2: Performance variation with change in parasitic to active elements
ratio (Change in M:N)
Fig. 9 shows the radiation pattern polar plot for the range ϴ = 0o
to
180o
, obtained by simulating our antenna design on FEKO. The
same can be validated in Figure 6 which is the array factor pattern
for a non-uniform 4 element array with Dolph-Chebyshev
coefficients obtained on MATLAB. Two anomalies in Figure 6,
which are the back lobe and two sidelobes, can be explained due to
lack of ground plane and the array of parasitic elements while
computing on MATLAB. This is understandable as the parasitic
array serves to bring side lobes down and increase the gain.
However, general shape of curve remains same.
VI. APPLICATION (DOA ESTIMATION)
Having obtained a pattern and the ability to synthesise one, our
antenna array system can be used for beam steering purpose to
estimate the direction of arrival. The resolution with which the
beam is steered further depends on the phase excitation
coefficients. An illustration of beamsteering is shown in Fig. 6
Figure 6: Beam Steering
We have seen that there is one-to-one relationship between the
direction of a signal and the associated received steering vector. It
should therefore be possible to invert the relationship and estimate
the direction of a signal from the received signals. An antenna
array therefore should be able to provide for direction of arrival
estimation. This serves as an application of the antenna array
system that we have designed above. The purpose of DOA
estimation is to use the data received by the array to estimate the
direction of arrival of the signal. The results of DOA estimation are
then used by the array to design the adaptive beam former in such a
way as to maximize the power radiated towards the users and to
suppress the interference.
MUltiple SIgnal Classfication (MUSIC) is one of the DOA
algorithms which can be used to estimate the direction of arrival
with a high spatial resolution. The basic idea of MUSIC is that the
eigenvalues and eigenvectors of a signal covariance matrix are
used to estimate the DOAs of multiple signals received by the
antenna array. In this paper, we have used MATLAB©
to do some
simulations in order to determine which factors affect the DOA
estimation. A matlab program on basic MUSIC algorithm for DOA
estimation has been written for 4 elements with spacing of λ/2
between them and a plot of Spectrum Function P(Θ) vs Angle (Θ)
has been generated as shown below in Figure 13.
As can be seen from Figure 13, for a received signal at Θ = 450
,
using MUSIC a needle spectrum peak algorithm can be
constructed. It may well estimate the number and direction of the
incidence signal, which can be used to estimate the independent
signal source DOA effectively.
Figure 13: DOA estimation based on Music Algorithm
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